This invention relates to a digital distance relaying system in which digital signals are used to protect electric power systems.
Although many types of distance relays have been proposed, according to one type the absolute values of two vectors are compared with each other. FIG. 1 of the accompanying drawings shows one example of comparing reactance characteristics wherein the operating point of the relay is judged according to the following equation 1. EQU .vertline.V-IZ.vertline.&gt;.vertline.V.vertline. 1
where Z=.vertline.Z.vertline.&lt;90.degree., V and I represent voltage and current and Z an impedance in vector corresponding to the distance from the location of the relay to the limit of the protected area. In equation 1, it is possible to vary the inclination angle of the characteristic curve as desired by varying the angle of the set vector Z, thereby obtaining a blinder characteristic for power flow. FIGS. 2a and 2b are vector diagrams showing the application of the principle to mho characteristics. This operation is expressed by the following equation 2. FIG. 2a shows a case of K.noteq.1 representing an offset mho characteristic and FIG. 2b shows a case of K=1 showing a mho characteristic where K represents a constant. EQU K.vertline.IZ.vertline.&gt;.vertline.V-IZ.vertline. 2
where Z=.vertline.Z.vertline.&lt;.theta. and .theta. represents the maximum sensitivity angle.
FIG. 3 is a block diagram showing an electric circuit of this invention for obtaining the reactance characteristic shown in FIG. 1. In FIG. 3, 11 and 12 show circuit elements which sample input voltage and current signals at a definite interval and hold and convert sampled analogue signals into digital signals. A vector synthesizer 13 is connected to the output of the element 12 for producing a vector IZ. A vector synthesizer 14 is connected to the outputs of the elements 11 and 12 to produce an output V-IZ. Amplitude value operators 15 and 16 are respectively connected to the outputs of element 11 and vector synthesizer 14 for obtaining the absolute values of the vectors shown in equation 1 by determining the amplitude values of the input alternating current data. The outputs of the amplitude value operators 15 and 16 are compared by a comparator 17 to judge that whether equation 1 holds or not. When equation 1 holds, the comparator 17 produces an output which is used to actuate the relay system.
FIG. 4 is a block diagram showing a circuit of this invention for obtaining the mho or offset mho characteristic shown in FIGS. 2a and 2b. There are provided sample/hold and A/D converting elements 21 and 22 similar to the elements 11 and 12 shown in FIG. 3 and vector synthesizers 23 and 24 which are similar to vector synthesizers 13 and 14 shown in FIG. 2 and form vectors IZ and V-IZ respectively. There are also provided amplitude value operators 25 and 26 which produce the absolute values of the input vectors similar to the amplitude value operators 15 and 16 shown in FIG. 2. The output of the amplitude value synthesizer 26 is multiplied by a constant K by a multiplier 27. Where K=1 and a mho characteristic is desired it is necessary to provide a memory action for nearby faults. To this end it is necessary to use voltage data one cycle before. A comparator 28 is used to compare the outputs of the amplitude value operator 25 and the multiplier 27 to perform the judgment shown by equation 2.
As the amplitude value calculating operations made by operators 15 and 16 shown in FIG. 3 and the operators 25 and 26 shown in FIG. 4, there have been used amplitude squaring method and rectification-addition method.
The amplitude squaring method utilizes the principle expressed by EQU sin.sup.2 .omega.t+cos.sup.2 .omega.t=sin.sup.2 .omega.t+sin.sup.2 (.omega.t+90.degree.)=1
Thus, two sampled values of the input AC quantity having a phase difference of 90.degree. are used and the sum of their squares is calculated to obtain the square of the amplitude value of the input AC quantity. The advantage of the amplitude squaring method lies in that the amplitude value can be obtained from a minimum of two sampled values and that it does not accompany any calculation error as a principle. On the other hand, there is a defect that it is necessary to calculate squares or square roots during calculation. When such calculations are made by a digital computer, calculations for multiplication, division and square roots require much longer time than mere addition and subtraction operations.
According to the rectification-addition method the absolute values of the sampled values corresponding to one half cycle or an integer multiple thereof of the input AC quantity are added together. For example, where the frequency of the input AC is 50 Hz and the sampling frequency is 600 Hz (a sampling interval of 30.degree.) the added value is shown by the following equation ##EQU1##
When a periodicity is considered, the value of equation (3-1) is included in a range shown by the following equation. ##EQU2## where 0.ltoreq..omega.t.ltoreq.15.degree..
According to this method, although it is possible to calculate the absolute value only by addition operations, it is necessary to use a number of sampled values (in the above described example, (6). Furthermore, there is a calculation error caused by the sampling times. In the illustrated example, this error varies about .+-.1.7% about the center of variation.
The following method has been proposed to eliminate the defects of said two prior art methods, which is expressed by ##EQU3## where i represents a time series, and h the number of samplings in one cycle. In other words, Si and Si+(h/4) represent sampled values having a phase difference of 90 electric degrees. For simplicity, let us assume that the original wave Si is a sine wave having an amplitude value of unity. Then equation 4 can be rewritten as follows. ##EQU4## where the periodicity is considered the range in which the value E shown by equation 5 is included is shown by the following equation. ##EQU5## The values of E calculated by equation 6 are shown in FIG. 5a. When constant K is selected to be 0.414, .alpha. becomes .alpha.=67.5.degree. and the values of E calculated by equation 6 are shown in FIG. 5b which shows that the error due to the sampling time is a minimum. Under these conditions the error about the center of variation of the value of E is .+-.3.96%. Although this method is superior than said two methods in that the amplitude value can be calculated by adding together only two sampled values, it is defective in that the operation error is larger.